Best Known (131, 131+37, s)-Nets in Base 8
(131, 131+37, 1822)-Net over F8 — Constructive and digital
Digital (131, 168, 1822)-net over F8, using
- net defined by OOA [i] based on linear OOA(8168, 1822, F8, 37, 37) (dual of [(1822, 37), 67246, 38]-NRT-code), using
- OOA 18-folding and stacking with additional row [i] based on linear OA(8168, 32797, F8, 37) (dual of [32797, 32629, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(8168, 32800, F8, 37) (dual of [32800, 32632, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(30) [i] based on
- linear OA(8161, 32768, F8, 37) (dual of [32768, 32607, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(8136, 32768, F8, 31) (dual of [32768, 32632, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(87, 32, F8, 5) (dual of [32, 25, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- construction X applied to Ce(36) ⊂ Ce(30) [i] based on
- discarding factors / shortening the dual code based on linear OA(8168, 32800, F8, 37) (dual of [32800, 32632, 38]-code), using
- OOA 18-folding and stacking with additional row [i] based on linear OA(8168, 32797, F8, 37) (dual of [32797, 32629, 38]-code), using
(131, 131+37, 33442)-Net over F8 — Digital
Digital (131, 168, 33442)-net over F8, using
(131, 131+37, large)-Net in Base 8 — Upper bound on s
There is no (131, 168, large)-net in base 8, because
- 35 times m-reduction [i] would yield (131, 133, large)-net in base 8, but